Question

find the equation of a line which is equidistant from the lines x=-2 and x=6

Answer 1

The lines x = − 2 and x = 6 pass through the points (−2, 0) and (6, 0), respectively.
Let (h, k) be the mid-point of the line joining the points (−2, 0) and (6, 0).

∴ h, k=(-2+6)/2, (0+0)/2,  so,h=2 and k =0

The given lines are parallel to the y-axis and the required line is equidistant from theses lines.
Hence, the required line is parallel to the y-axis, which is given by x = k.

This line passes through (2, 0).

∴ 2 = k
⇒ k = 2

Hence, the equation of a line that is equidistant from the lines x = − 2 and x = 6 is x = 2.

Answer 2

Answer:

The equation of equation line is x=2.

Step-by-step explanation:

The given lines are

x=-2

x=6

Both lines are in the form of x=a. It means these are vertical lines with y-intercept a.

If a line is equidistant from the lines x=-2 and x=6. It means It is also a vertical line which is passing though the midpoints of y-intercepts of both the lines.

It means first line passing though (-2,0) and second line passing through (6,0).

Midpoint of (-2,0) and (6,0) is

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{-6+2}{2},\frac{0+0}{2})=(2,0)$

The required line passing through the point (2,0). Since it is a vertical line, therefore the equation of equation line is x=2.